Lectures related to Nonlinear Problem Solving

Numerical Methods: Iterative Techniques

Covers open methods, Newton-Raphson, and secant method for iterative solutions in numerical methods.

Computational Geomechanics: Unconfined Flow

Explores unconfined flow in computational geomechanics, emphasizing weak form derivation and relative permeability.

Attack on RSA using LLL

Covers Coppersmith's method for attacking RSA encryption by efficiently finding small roots of polynomials modulo N.

Numerical Methods in Chemistry

Covers the implementation of numerical methods in MATLAB for solving chemical problems.

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Numerical Derivation: Formulas and Approaches

Covers the numerical approach to derivative calculation, focusing on formulas and methods such as fine differences.

Numerical Methods in Biomechanics: Hip-A

Explores numerical methods in biomechanics for hip implants and emphasizes understanding conditions for improved designs and patient outcomes.

Numerical Differentiation: Part 1

Covers numerical differentiation, forward differences, Taylor's expansion, Big O notation, and error minimization.

Neutron Diffusion Equation: Numerical Methods

Covers numerical methods for solving the neutron diffusion equation and addressing heterogeneous effects in thermal reactors.

Multigroup Theory: Main Equations and Numerical Solution

Covers the derivation of multi-group diffusion equations and the numerical methods for solving the neutron diffusion equation.

Root Finding Methods: Bisection and Secant Techniques

Covers root-finding methods, focusing on the bisection and secant techniques, their implementations, and comparisons of their convergence rates.

Inverse Power Method: Introduction to ODEs

Explores the inverse power method for ODEs and the significance of Lipschitz continuity.

Numerical Modelling of the Atmosphere

Focuses on numerical modelling of atmospheric processes to predict weather and climate phenomena, covering key concepts and methods.

ODEs: Introduction and Solutions

Covers Ordinary Differential Equations, first-order solutions, and numerical methods for IVP and BVP.

Thomas algorithm, accuracy of direct methods

Explores the Thomas algorithm for tridiagonal systems and the accuracy of direct methods in numerical computations.

Finite Elements: Elasticity and Variational Formulation

Explores finite element methods for elasticity problems and variational formulations, emphasizing admissible deformations and numerical implementations.

Numerical Methods: Bisection and Multidimensional Arrays

Discusses the bisection method for solving nonlinear equations and its implementation using Python with NumPy and Matplotlib.

Sensitivity of Solutions

Explores the sensitivity of solutions in numerical methods, including linear systems and matrix norms, with an example of deblurring images.

Numerical Integration: Lagrange Interpolation, Simpson Rules

Explains Lagrange interpolation for numerical integration and introduces Simpson's rules.

Numerical Integration: Romberg Integration

Explores Romberg integration to improve numerical integration accuracy through iterative refinement of estimates.